Signal processing generally encompasses collecting, organizing, transforming and summarizing raw input data to produce meaningful or useful information, or output data. Signal processing typically manipulates large amounts of numeric data, and may include processes such as sorting, formatting, aggregation, classification, validation, and reporting the data.
A delay embedding theorem specifies the conditions under which a chaotic dynamical system may be reconstructed from a sequence of observations of the state of a dynamical system. In general, the reconstruction should preserve the properties of the dynamical system that do not change under smooth coordinate changes, but not necessarily the geometric shape of structures in phase space. For example, Takens' theorem (1981) provides a delay embedding theorem that provides the conditions under which the underlying dynamics of a physical system may be reconstructed from an observed time series, given a sufficient number of observations at equally spaced times.
Cardiovascular periodicity generally refers to the nearly regular, recurrent blood pressure and volume pulses induced by the heart. The time length of each period between consecutive individual heart beats is commonly referred to as the interbeat interval (IBI, or RR interval). The heart rate is the inverse of the cardiovascular periodicity.
During normal heart functioning, there is some variation in the continuous time series of IBI values. This natural variation is known as heart rate variability (HRV). Relatively noisy or low-amplitude sensor signals may add measurement error that further detracts from the nearly periodic nature of the observed heart beat signal. Thus, the observed heart beat sensor signal typically represents a quasiperiodic function. That is, the signal is similar to a periodic function, but displays irregular periodicity and does not meet the strict definition of a periodic function that recurs at regular intervals. Quasiperiodic behavior includes a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement.
The time intervals between consecutive heart beats are customarily measured in an electrocardiogram (ECG or EKG) from the initiation of each of two consecutive QRS complexes, corresponding to the contraction of the heart ventricles, each of which typically includes three component waveforms (the Q-wave, R-wave and S-wave). However, the initiation of the QRS complex may be difficult to locate in relatively noisy or low-amplitude sensor signals, which may lead to measurement error. Thus, IBI is sometimes measured between R-wave peaks in consecutive heart beats to reduce measurement error.
IBI may also be determined from a peripheral pulse measurement, such as a digital volume pulse measurement, such as a photoplethysmogram (PPG), an optically obtained plethysmogram, or volumetric measurement of an organ. PPG sensors have been used to monitor respiration and heart rates, blood oxygen saturation, hypovolemia, and other circulatory conditions.
The pulse oximeter, a known type of PPG sensor, illuminates the skin with one or more colors of light and measures changes in light absorption at each wavelength. The PPG sensor illuminates the skin, for example, using an optical emitter, such as a light-emitting diode (LED), and measures either the amount of light transmitted through a relatively thin body segment, such as a finger or earlobe, or the amount of light reflected from the skin, for example, using a photodetector, such as a photodiode.
Conventional PPGs typically monitor the perfusion of blood to the dermis and subcutaneous tissue of the skin, which may be used to detect, for example, the change in volume corresponding to the pressure pulses of consecutive cardiac cycles of the heart. If the PPG is attached without compressing the skin, a secondary pressure peak may also be seen from the venous plexus. A microcontroller typically processes and calculates the peaks in the waveform signal to count heart beats per minute (bpm).
Lorenz, or Poincaré, plots of RR intervals, in which each data point represents a pair of successive beats, with the current RR interval plotted against the previous RR interval, have been used as a geometric or graphical non-linear method to evaluate HRV. These plots permit visualization of higher-dimensional phase spaces in subspaces with relatively low dimensionality, for example, two- or three-dimensional subspaces. In some analyses, mathematically-defined geometric shapes—such as elliptic, linear, or triangular shapes—have been fitted to the overall data pattern. In other analyses, the dispersion of points along or orthogonal to the axis of the identity line, or line of equality, has been evaluated.